Multi-Stage Sub-THz Frequency Generator Incorporating Injection Locking

ABSTRACT

A novel and useful mm-wave frequency generation system is disclosed that takes advantage of injection locking techniques to generate an output oscillator signal with improved phase noise (PN) performance and power efficiency. Low frequency and high frequency DCOs as well as a pulse generator make up the oscillator system. A fundamental low frequency (e.g., 30 GHz) signal and its sufficiently strong higher (e.g., fifth) harmonic (e.g., 150 GHz) are generated simultaneously in a single oscillator system. The second high frequency DCO having normally poor phase noise is injected locked to the first low frequency DCO having good phase noise. Due to injection locking, the high frequency output signal generated by the second DCO exhibits good phase noise since the phase noise of the second DCO tracks that of the first DCO.

REFERENCE TO PRIORITY APPLICATION

This application claims priority to U.S. Provisional Application Ser.No. 62/621,611, filed Jan. 25, 2018, entitled “Multi-Stage Sub-THzFrequency Generator Using Injection Locking,” incorporated herein byreference in its entirety.

FIELD OF THE INVENTION

The present invention relates to the field of semiconductor integratedcircuits and more particularly relates to a multi-stage sub-THzfrequency generator that utilizes injection locking techniques.

BACKGROUND OF THE INVENTION

High frequency oscillators are the key blocks in mm-wave front-endcircuits which are mainly focusing on short-range high-speed links(e.g., IEEE 802.1 lad/y, mm-wave 5G), FMCW automotive radars (e.g.,76-81 GHz), and imaging and security applications above 100 GHz.Currently, many high frequency oscillators are typically implemented insilicon/germanium (SiGe) technology due to wider RF passive devicessupport, higher speeds over earlier CMOS nodes, and potential basebandintegration through BiCMOS extensions which are more expensive comparedto CMOS technology. On the other hand, designing high speed oscillatorsin CMOS technology is much more challenging since the quality factor ofpassive components are lower than other technology.

There is thus a need for a high frequency oscillator that does notsuffer from the disadvantages of the prior art. The oscillator shouldhave improved phase noise and power efficiency and not require use of abuffer or amplifier at the output.

SUMMARY OF THE INVENTION

A novel and useful mm-wave frequency generation system is disclosed thattakes advantage of injection locking techniques to generate an outputoscillator signal with improved phase noise (PN) performance and powerefficiency. A fundamental low frequency (e.g., ˜30 GHz K-band) signaland its sufficiently strong higher (e.g., fifth) harmonic at a highfrequency (e.g., ˜150 GHz D-band) are generated simultaneously in asingle oscillator.

Several features and advantages of the oscillator architecture of thepresent invention includes: (1) injecting pulse generator harmonics to afirst oscillator; (2) injecting the higher (e.g., fifth) harmonic to asecond oscillator; (3) generating higher (e.g., fifth) harmonics inclass F; (4) injecting the higher (e.g., fifth) harmonic of class F to asecond oscillator rather than extract it; and (5) not requiring a bufferand delivering maximum power at a relatively high frequency and withoutthe need for a power hungry power amplifier.

Note that the oscillator architecture of the present invention has beenimplemented in 28 nm CMOS technology. Using the circuit structuredescribed herein, the total power consumption of the system isapproximately 40 mW while it delivers 1.7 dBm output power at 150 GHz.As a result, a very low phase noise oscillator with high powerefficiency can be achieved using CMOS technology.

The oscillator system described herein is suitable for automotive radar,phased array, imaging, and security applications since it exhibits verygood phase noise and output power. Moreover, since it providesrelatively high output power at 150 GHz with tight coupling to the 30GHz stage, it can be directly connected to an antenna and function as apower amplifier. In addition, due to its low power consumption, theoscillator system can be used in systems which need to save power.

There is thus provided in accordance with the invention, an oscillatorsystem, comprising a reference frequency pulse generator operative togenerate a reference signal containing a plurality of harmonics, a firstoscillator operative to receive said reference signal output by saidpulse generator and to generate a first fundamental frequency and one ormore harmonic signals therefrom, wherein said first oscillator isinjection locked to said pulse generator, and a second oscillatoroperative to receive one of the harmonic signals output by said firstoscillator, and to generate an output signal therefrom, wherein saidsecond oscillator is injection locked to said first oscillator.

There is also provided in accordance with the invention, an oscillatorsystem, comprising a pulse generator having relatively good phase noiseoperative to generate a reference frequency signal containing aplurality of harmonics, a first oscillator operative to generate amillimeter wave output fundamental signal along with a higher harmonicsignal, wherein said first oscillator is injection locked to saidreference frequency signal output of said pulse generator, and a secondoscillator normally having relatively poor phase noise operative togenerate an output oscillator signal at an output node having relativelygood phase noise, wherein said second oscillator is injection locked tosaid first oscillator causing the phase noise of said second oscillatorto track that of said first oscillator.

There is further provided in accordance with the invention, a method ofgenerating an oscillator signal, comprising generating a referencefrequency signal, first injection locking a first oscillator and to thereference frequency signal thereby generating a millimeter wave firstoscillator signal along with a harmonic signal, wherein phase noise ofsaid first oscillator tracks that of said reference frequency signal,and second injection locking a second oscillator to the harmonic signaland generating an output oscillator signal therefrom at an output node,and wherein the phase noise of said second oscillator tracks that ofsaid first oscillator.

There is also provided in accordance with the invention, an oscillatorsystem, comprising a pulse generator having relatively good phase noiseoperative to generate a reference frequency signal having a plurality ofharmonics, a first oscillator operative to receive the referencefrequency signal and to generate a fundamental signal along with ahigher harmonic signal therefrom, wherein said first oscillator isinjection locked to the reference frequency signal output of said pulsegenerator, a second oscillator normally operative to generate a firstoutput oscillator signal at an output node, wherein said secondoscillator is injection locked to said first oscillator causing thephase noise of said second oscillator to track that of said firstoscillator, and a third oscillator operative to generate a second outputsignal, wherein said third oscillator indirectly injection locked tosaid reference frequency signal output of said pulse generator causingthe phase noise of said third oscillator to track that of said pulsegenerator.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is explained in further detail in the followingexemplary embodiments and with reference to the figures, where identicalor similar elements may be partly indicated by the same or similarreference numerals, and the features of various exemplary embodimentsbeing combinable. The invention is herein described, by way of exampleonly, with reference to the accompanying drawings, wherein:

FIG. 1 is a high-level block diagram illustrating an example highfrequency oscillator employing multiplier techniques;

FIG. 2 is a high-level block diagram illustrating an example highfrequency oscillator employing push-push techniques;

FIG. 3 is a high-level block diagram illustrating an example fundamentalhigh frequency oscillator;

FIG. 4 is a high-level block diagram illustrating an example multi-stagehigh-frequency oscillator utilizing injection locking techniques;

FIG. 5 is a schematic diagram illustrating an example multi-stagehigh-frequency oscillator utilizing injection locking techniques;

FIG. 6 is a schematic diagram illustrating an example pulse generator;

FIG. 7 is a schematic diagram illustrating an example multi-stage dualhigh-frequency oscillator utilizing injection locking techniques;

FIG. 8 is a schematic diagram illustrating an example transformercircuit;

FIG. 9 is a diagram illustrating X-factor versus harmonic ratio fordifferent values of k_(m);

FIG. 10 is a diagram illustrating the dependency of X-factor on k_(m);

FIG. 11 is a diagram illustrating the dependency of tank inputresistance on k_(m);

FIG. 12 is a diagram illustrating the dependency of equivalent qualityfactor of transient based resonant at 30 GHz on k_(m);

FIG. 13 is a diagram illustrating the drain current of the 30 GHzoscillator with strengthened 5^(th) harmonic;

FIG. 14 is a diagram illustrating the dependency of the normalizedresonance frequency on k_(m);

FIG. 15 is a diagram illustrating the primary and secondary inductanceas a function of frequency;

FIG. 16 is a diagram illustrating the primary and secondary qualityfactor (Q) as a function of frequency;

FIG. 17 is a diagram illustrating the transformer coupling factor as afunction of frequency;

FIG. 18 is a diagram illustrating the oscillator voltage waveform indifferential mode;

FIG. 19 is a diagram illustrating the oscillator gate voltage waveform;

FIG. 20 is a diagram illustrating the transformed-based tank inputimpedance Z₁₁ magnitude;

FIG. 21 is a diagram illustrating the transformed-based tanktrans-impedance Z₂₁ magnitude;

FIG. 22 is a diagram illustrating an example ratio of fifth harmonic tofundamental magnitude;

FIG. 23 is a diagram illustrating example phase noise for the oscillatorcircuit of FIG. 5;

FIG. 24 is a diagram illustrating a first example locked signal spectrumof the oscillator system; and

FIG. 25 is a diagram illustrating a second example locked signalspectrum of the oscillator system.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is a novel and useful mm-wave frequency generationsystem that takes advantage of injection locking techniques to generatean output oscillator signal with improved phase noise (PN) performanceand power efficiency. A fundamental low frequency (e.g., 30 GHz) signaland its sufficiently strong higher (e.g., fifth) harmonic at a highfrequency (e.g., 150 GHz) are generated simultaneously in a singleoscillator.

A high-level block diagram illustrating an example high frequencyoscillator employing a multiplier technique is shown in FIG. 1. In thisembodiment, the oscillator, generally referenced 10, comprises arelatively low frequency reference 12 (150/m GHz). This reference ismultiplied m times via frequency multiplier block 14. The output isbuffered and amplified via amplifier 16 to generate the desiredoscillator output frequency (150 GHz in this example). Oscillators basedon frequency multipliers at this high frequency typically have limitedlocking range or consume large amounts of power in order to achievelarge locking range.

A high-level block diagram illustrating an example high frequencyoscillator employing a push-push technique is shown in FIG. 2. In thisexample, the oscillator, generally referenced 20, comprises a 150/m GHzpush-push oscillator block 22 containing m-push oscillators. Thepush-push technique is used to obtain oscillation at high frequencies.The output of block 22 is buffered and amplified via amplifier 24 togenerate the desired oscillator output frequency (150 GHz in thisexample).

An oscillator with m-push oscillators utilize frequency dividersoperating at 150/m GHz, avoiding the use of frequency multipliers. Thisoscillator type, however, suffers from low output power and mismatchesamong the m oscillators. Among this type, push-push oscillators are themost common and easiest to implement. The required large common mode(CM) swing, however, can increase the 1/f noise upconversion. Moreover,the conversion from single-ended CM signal to a differential output mayintroduce large phase error.

Both of these oscillator circuits, suffer from high power consumptionand low output power. Thus, the power efficiency of these oscillatorcircuit techniques is a significant bottleneck to using them in realworld applications.

A high-level block diagram illustrating an example fundamental highfrequency oscillator is shown in FIG. 3. As shown in FIG. 3, theoscillator, generally referenced 30, comprises a high frequencyreference 32 (e.g., 150 GHz), and amplifier 34 which functions togenerate the oscillator output at a high fundamental frequency. This isone of the first requirements of designing a high-speed oscillator. Thistechnique, however, is not sufficient at high frequency where it isrestricted by the f_(max) of the semiconductor process devices used toconstruct to the oscillator. Thus, the phase noise and gain requirementsare not met. Moreover, the quality factor of passive componentsdeteriorates at relatively high frequencies.

Several difficulties of designing oscillators of the type describedsupra include (1) the parasitic capacitance of active devices takes up alarge share of the relatively small tank capacitance, thus limiting thefrequency tuning range; (2) to achieve a tuning range of >15%, the poorQ-factor of the tuning capacitance dominates the Q-factor of theresonator, thus limiting the achievable phase noise. The 150 GHzfrequency dividers must achieve large locking range to ensure sufficientoverlap with the oscillator tuning range under PVT variations. There isa strong tradeoff, however, between the locking range and the powerconsumption.

To alleviate the design challenges for mm-wave oscillators and dividerswithout shifting more stress onto other blocks, a 150 GHz frequencygeneration technique based on a 30 GHz oscillator and higher (e.g.,fifth) harmonic is disclosed. To realize that goal, the higher (e.g.,fifth) harmonic as well as the fundamental are applied to a 30 GHztransformer-based dual-resonance oscillator. Using this technique, thehigher (e.g., fifth) harmonic is the signal of interest.

In accordance with the invention, both a low frequency fundamental(e.g., 30 GHz) and a significant level of its higher (e.g., fifth)harmonic at a high frequency (e.g., 150 GHz) are simultaneouslygenerated within a low frequency, e.g., 30 GHz, oscillator. Thegenerated 150 GHz signal is fed to a second high frequency oscillator.Since, in one embodiment, the oscillator runs at the fundamentalfrequency of 30 GHz, its resonant tank achieves a better Q-factor thanat 150 GHz, which leads to better PN performance. Moreover, the tank hasa larger inductance and capacitance. This increases the variable portionof the total tank capacitance and the frequency tuning range.

A high-level block diagram illustrating an example multi-stagehigh-frequency oscillator utilizing injection locking techniques isshown in FIG. 4. The oscillator, generally referenced 40, comprisespulse generator 42, first low frequency digitally controlled oscillator(DCO) 44, and second high frequency DCO 46. The second DCO is operativeto generate and output the target frequency (150 GHz in this exampleembodiment).

In this example embodiment, the oscillator architecture is based on aninjection locking technique. The pulse generator 42 functions as areference frequency. This eases the design of the frequency divider whenthe oscillator 40 is used to implement a phase locked loop (PLL). Thepulse generator is operative to generate one or more harmonics (nharmonics in this example). The low frequency DCO 44 is injection lockedto one of the harmonics generated by the pulse generator. In thisexample embodiment, the pulse generator fundamental period is 60 pswhich corresponds to approximately 16 GHz. The second harmonic at 32 GHzis injection locked to the first low frequency DCO.

In one embodiment, the first DCO comprises a 30 GHz oscillator such as aclass F oscillator adapted to produce relatively strong 5th harmonics at150 GHz. Since the first oscillator is injection locked to the pulsegenerator which is designed to exhibit relative very good phase noise,the first oscillator output signal (i.e. fundamental as well asharmonics) also has relatively very clean phase noise as well.

The second DCO comprises a relatively high frequency oscillator circuit.In one example, the second oscillator is adapted to generate a 150 GHzsignal. The second DCO, however, is designed to normally exhibitrelatively poor phase noise performance, i.e. when the DCO isstand-alone without any injection locking in order to conserve power.The signal output of the class F oscillator (i.e. first DCO) isinjection locked to the second oscillator which normally features poorphase noise. Note that the strong 5th harmonic of the first oscillatorcan be injected simultaneously with the fundamental frequency (e.g., 30GHz) signal to the second oscillator stage, i.e. the high frequencyoscillator which in this example embodiment is 150 GHz. This causes thesecond 150 GHz oscillator to lock relatively easily to the first 30 GHzoscillator. Consequently, the second high frequency oscillator tracksthe phase noise of the first oscillator within a relatively wide lockingrange.

Thus, using this injection locking technique relaxes the designchallenges of the second oscillator at 150 GHz at least from a phasenoise point of view. Since the injection signal generated by the firstoscillator is strong, the second oscillator having wide locking range islocked to the first oscillator and tracks its phase noise. Moreover,since the second oscillator (e.g., 150 GHz) is used as the output stageinstead of a multiplier in the architecture described supra, it providesrelatively high output voltage swing and high output power at 150 GHzwhile consuming less power.

A schematic diagram illustrating the circuit implementation of anexample multi-stage high-frequency oscillator utilizing injectionlocking techniques is shown in FIG. 5. The injection oscillatorfunctions to boost the higher (e.g., fifth) harmonic generated by thefirst DCO. The oscillator, generally referenced 50, comprises twosub-oscillators including a low frequency oscillator 56 (e.g., 30 GHz)and a high frequency oscillator 58 (e.g., 150 GHz). The low frequencyoscillator 56 comprises transformer 57 based tank while the highfrequency oscillator 58 comprises transformer 59 based tank.

The class F low frequency oscillator 56 comprise transistors M₁ and M₂and is adapted to produce relatively strong 5^(th) harmonics. Using theinjection transistors M_(inj), the 5^(th) harmonics of the low frequencyoscillator 56 is injected to the second stage high frequency oscillator58 via transistors M₃ and M₄ which in one example embodiment comprises a150 GHz oscillator normally having relatively poor phase noise. At theoutput stage, in order to separate the output node from pad parasiticsand also deliver maximum power to output, transformer 59 with couplingfactor k_(m2) is used. Note that a load-pull simulation has beenperformed at the output stage to determine the required impedance whichprovides both oscillation and delivers maximum power to the output node.

In one embodiment, a 1:2 transformer (k_(m)=0.67) together withbinary-weighted switched MOM capacitor banks in both primary andsecondary windings of transformer 57 comprises the resonant tank at lowfrequency DCO 56 (30 GHz) which functions to provide a relatively strong5^(th) harmonic. By changing the separation space between primary andsecondary windings, k_(m) is adjusted to the desired value. CapacitorC_(s) provides coarse tuning, while C_(p) adjusts the second resonanceclose to 5ω_(osc). In the 150 GHz output of the second stage of theoscillator 50, the output buffer has been removed and a transformer isused at this node, i.e. the drain of the 150 GHz oscillator. Thus, theoscillator nodes are separated from the 50 ohm pad and, in addition, bydesigning the correct impedance, the maximum power is delivered to theoutput, e.g., 1.75 dBm at 150 GHz in one embodiment. This is one of thebenefits of the oscillator of the present invention since it relaxes thedesign requirements for the power amplifier in a transmitter circuit andalso increases the power added efficiency in the transmitter structure.

In one embodiment, the L and C ratios in primary and secondary windingsof the transformer based dual tank resonator were optimized to realizefundamental oscillation and its higher (e.g., fifth) harmonic resonance.

A schematic diagram illustrating an example pulse generator is shown inFIG. 6. The pulse generator, generally referenced 60, comprises afrequency reference source 62 that may comprise a crystal oscillator(XO), an external frequency reference, e.g., having sinusoidal shape,etc., or a ring oscillator. The pulse generator is operative to generatean output reference signal 64 having any desired pulse width inaccordance with the particular implementation of the invention, e.g.,10-30 or 55-70 ps.

In the example embodiment shown, the noise-free pulse generatorcomprises a crystal oscillator (XO) slicer that combines theprogrammable edge delay. The voltage offset ΔV gets converted to timeoffset ΔT (by adding extra offset-inducing transistors) by delaying thethreshold detection of the sinusoidal waveform. This mechanism does notappreciably add any extra noise. Note that the pulse width is controlledfrom 10-30 ps (or 55-70 ps) with a multibit code.

A schematic diagram illustrating an example multi-stage dualhigh-frequency oscillator utilizing injection locking techniques isshown in FIG. 7. In this additional embodiment, a dual mode 79/150 GHzband injection locked oscillator system is provided. The oscillatorsystem, generally referenced 70, comprises pulse generator 72, first lowfrequency digitally controlled oscillator (DCO) 74, second highfrequency DCO 76, third DCO 78, and buffer/amplifier 80. In one exampleembodiment, the first DCO runs at approximately 30 GHz, the second DCOat approximately 150 GHz, and the third DCO at approximately 83 GHz.

The third 79 GHz oscillator 78 is used in a second path which is lockeddirectly to the pulse generator 72. In this embodiment, the first pathis the same as the oscillator shown in FIG. 4, described in detailsupra. In the second path, the 83 GHz oscillator 78 is locked to 5^(th)harmonics generated by the pulse generator. The output of the oscillator78 is input to a buffer and/or amplifier to the output. Note that thisembodiment is capable of simultaneously providing dual oscillators inthe range of 145-165 GHz and 75-90 GHz for both FMCW automotive radars(e.g., 76-81 GHz) as well as imaging and security applications above 100GHz.

A schematic diagram illustrating an example transformer circuit is shownin FIG. 8. The transfer, generally referenced 90, comprises atransformer 92 with 1:n turns ratio and coupling factor k_(m), primaryL_(p) and secondary L_(p) windings, and tunable primary capacitor C₁ andsecondary capacitor C₂. To provide adequate 5^(th) harmonic signal, thetransformer 57 (FIG. 5) preferable has a relatively high coupling factork_(m).

A diagram illustrating X-factor versus harmonic ratio for differentvalues of k_(m) is shown in FIG. 9. The X-factor is defined as follows

$\begin{matrix}{X = \left( {\frac{L_{s}}{L_{p}} \cdot \frac{C_{2}}{C_{1}}} \right)} & (1)\end{matrix}$

Trace 100 represents the harmonic ratio for k_(m)=0.9; trace 102represents the harmonic ratio for k_(m)=0.8; and trace 104 representsthe harmonic ratio for k_(m)=0.7.

A diagram illustrating the dependency of X-factor on k_(m) when

$\frac{\omega_{5}}{\omega_{1}} = 5$

is shown in FIG. 10. Note that an X-factor of 12 corresponds to a k_(m)of 0.67. The required X-factor is used to select an appropriate value ofthe running capacitor.

A diagram illustrating the dependency of tank input resistance on k_(m)is shown in FIG. 11. Trace 110 represents R_(p5) while trace 112represents R_(p1). A diagram illustrating the dependency of equivalentquality factor of transient based resonant at 30 GHz on k_(m) is shownin FIG. 12. It is noted that the higher (e.g., fifth) harmonic componentgenerated by the first oscillator is the signal of interest. Thus, it ispreferable to make it sufficiently stronger by configuring a largerR_(p5)/R_(p1). On the other hand, however, the equivalent Q factor atthe two resonant frequencies affect oscillator performance. A high Qfactor at ω_(osc) (e.g., 30 GHz) promotes low phase noise, while low Qat 5ω_(osc) is appreciated for better tolerance to possible frequencymisalignment between the second resonance and 5ω_(osc). As shown in FIG.11, R_(p1) decreases with smaller k_(m) while R_(p5) behaves opposite.Therefore, smaller k_(m) is desired for large R_(p5)/R_(p1) and in doinga passive gain for the 5^(th) harmonic is provided. As shown in FIG. 12,however, a larger k_(m) is required for high Q at ω_(osc) to have betterphase noise.

In one embodiment, as a trade-off between a large higher (e.g., fifth)harmonic and optimal oscillator performance, k_(m)=0.67 is selected forR_(p5)/R_(p1)=2 with sufficient Q. A diagram illustrating the dependencyof the normalized resonance frequency on k_(m) is shown in FIG. 14 wheretrace 120 represents ω₅/30 and trace 122 represents ω₁/30. Under thiscondition, as the ratio of ω_(osc5)/ω_(osc1) reaches the desired valueof five for k_(m)=0.67 which corresponds to an X-factor of 12 (see FIG.11).

Intuitively, we know that the drain current of oscillator in thepresence of harmonics is close to a square wave as shown in FIG. 13which illustrates the drain current of the low frequency (e.g., 30 GHz)oscillator with strengthened 5^(th) harmonic. It is also known that anideal square wave with an amplitude of one can be represented as aninfinite sum of sinusoid waves:

$\begin{matrix}\begin{matrix}{{x(t)} = {\frac{4}{\pi}{\sum\limits_{k = 1}^{\infty}\frac{\sin \left( {2{\pi \left( {{2k} - 1} \right)}f\; t} \right)}{{2k} - 1}}}} \\{= {\frac{4}{\pi}{\left( {{\sin \left( {2\pi \; f\; t} \right)} + {\frac{1}{3}{\sin \left( {3*2\pi \; f\; t} \right)}} + {\frac{1}{5}{\sin \left( {5*2\pi \; f\; t} \right)}} + \ldots}\mspace{14mu} \right).}}}\end{matrix} & (2)\end{matrix}$

According to Equation 2, the higher (e.g., fifth) harmonic is a veryweak signal. Thus, having passive gain helps to inject a stronger higher(e.g., fifth) harmonic signal to the high frequency (e.g., 150 GHz)oscillator which improves the locking range of the oscillator system.This provide additional motivation to select a coupling factor ofk_(m)=0.67.

A diagram illustrating an example ratio of fifth harmonic to fundamentalmagnitude is shown in FIG. 22. As indicated, the output signal of thelow frequency oscillator (e.g., 30 GHz class F oscillator) providesrelatively strong fifth harmonics. Utilizing the passive gain boostedfifth harmonic, the magnitude ratio between fifth to first harmonicscomponents of the drain oscillator voltages increases to almost 10%.This high ratio provides a strong injected signal to the second stagehigh frequency oscillator (e.g., 150 GHz) and helps it to lock withlower power consumption as well as having a wider locking range.

A diagram illustrating the transformed-based tank input impedance Z₁₁magnitude is shown in FIG. 20. The figure shows the tank input impedancewith k_(m)=0.67. Note that a concern may arise that the oscillationcould happen at 5ω_(osc) (˜150 GHz) rather than at ω_(osc) (˜30 GHz) dueto Rp5>Rp1. Start-up conditions are examined to ensure that theoscillation can only happen at ω_(osc), even if R_(p5)>R_(p1).Barkhausen's phase and gain criteria should be satisfied for a stableoscillation.

A diagram illustrating simulated open loop response of thetransformed-based tank trans-impedance Z₂₁ magnitude is shown in FIG.21. This figure shows the open loop phase response of transimpedanceZ₂₁. Note that the phase criterion is satisfied only at ω_(osc) whichshows that there only one stable oscillation mode at ˜30 GHz is possiblehere.

$\begin{matrix}{Z_{in} = \frac{\begin{matrix}{{s^{3}\left( {L_{p}L_{s}{C_{2}\left( {1 - k_{m}^{2}} \right)}} \right)} +} \\{{s^{2}\left( {C_{2}\left( {{L_{s}r_{p}} + {L_{p}r_{s}}} \right)} \right)} + {s\left( {L_{p} + {r_{s}r_{p}C_{2}}} \right)} + r_{p}}\end{matrix}}{\begin{matrix}{{s^{4}\left( {L_{p}L_{s}C_{1}{C_{2}\left( {1 - {km}^{2}} \right)}} \right)} + {s^{3}\left( {C_{1}{C_{2}\left( {{L_{s}r_{p}} + {L_{p}r_{s}}} \right)}} \right)} +} \\{{s^{2}\left( {{L_{p}C_{1}} + {L_{s}C_{2}} + {r_{p}r_{s}C_{1}C_{2}}} \right)} + {s\left( {{r_{p}C_{1}} + {r_{s}C_{2}}} \right)} + 1}\end{matrix}}} & (3)\end{matrix}$

where k_(m), Lp, Ls, C₁, C₂, r_(p), and r_(s) are the magnetic couplingfactor of the transformer, primary and secondary inductance, tuningcapacitor on the primary and secondary side, and model the equivalentseries resistance of the primary and secondary inductance, respectively.In order to find the poles of this transfer function, the equation issolved for the denominator=0 which yields

$\begin{matrix}{\omega_{1,2}^{2} = \frac{1 + {\frac{L_{s}C_{2}}{L_{p}C_{1}} \pm \sqrt{1 + \left( \frac{L_{s}C_{2}}{L_{p}C_{1}} \right)^{2} + {\frac{L_{s}C_{2}}{L_{p}C_{1}}\left( {{4k_{m}^{2}} - 1} \right)}}}}{2L_{s}{C_{2}\left( {1 - k_{m}^{2}} \right)}}} & (4)\end{matrix}$

Since we are interested in the higher (e.g., fifth) harmonic, the ratio

${\frac{\omega_{2}}{\omega_{1}} = 5},$

as a result is given by

$\begin{matrix}{\frac{\omega_{2}}{\omega_{1}} = {\sqrt{\frac{1 + X + \sqrt{1 + X^{2} + {X\left( {{4k_{m}^{2}} - 2} \right)}}}{1 + X - \sqrt{1 + X^{2} + {X\left( {{4k_{m}^{2}} - 2} \right)}}}} = 5}} & (5)\end{matrix}$

where

$X = {\left( {\frac{L_{s}}{L_{p}}\frac{C_{2}}{C_{1}}} \right).}$

By solving Equation 5, we obtain X as a function of k_(m), as shown inFIG. 9.

To determine R_(p1) and R_(p5), the real part of Equation 3 must bedetermined first as follows

$\begin{matrix}{{\left\{ {Z_{in}(\omega)} \right\}} = \frac{{\left. \left( {r_{p} - {\omega^{2}A}} \right) \right)\left( {{C_{1}B\; \omega^{4}} - {C\; \omega^{2}} + 1} \right)} + {{\omega^{2}\left( {D - {B\; \omega^{2}}} \right)}\left( {E - {C_{1}A\; \omega^{2}}} \right)}}{\left( {{C_{1}B\; \omega^{4}} - {C\; \omega^{2}} + 1} \right)^{2} + \left( {E - {C_{1}A\; \omega^{2}}} \right)^{2}}} & (6)\end{matrix}$

where A, B, C, D, and E are calculated as follows

A=C ₂(L _(s) r _(p) +L _(p) r _(s))

B=L _(p) L _(s) C ₂(1−k _(m) ²)

C=L _(p) C ₁ +L _(s) C ₂ +r _(p) r _(s) C ₁ C ₂

D=(L _(p) +r _(s) r _(p) C ₂)

E=(r _(p) C ₁ +r ₈ C ₂)  (7)

R_(p1) and R_(p5) are calculated as R_(p1)=

{Z_(in)(ω₁}, R_(p5)=

{Z_(in)(ω₂} where it is known that ω₂=5ω₁. The results are shown in FIG.11.

The transimpedance of the tank from primary to secondary winding is asfollows

$\begin{matrix}{{Z_{21}\left( {j\; \omega} \right)} = \frac{j\; \omega \; k_{m}\sqrt{L_{p}L_{s}}}{\begin{matrix}{{\omega^{4}\left( {L_{p}L_{s}C_{1}{C_{2}\left( {1 - {k\; m^{2}}} \right)}} \right)} - {j\; {\omega^{3}\left( {C_{1}{C_{2}\left( {{L_{s}r_{p}} + {L_{p}r_{s}}} \right)}} \right)}} -} \\{{\omega^{2}\left( {{L_{p}C_{1}} + {L_{s}C_{2}} + {r_{p}r_{s}C_{1}C_{2}}} \right)} + {j\; {\omega \left( {{r_{p}C_{1}} + {r_{s}C_{2}}} \right)}} + 1}\end{matrix}}} & (8)\end{matrix}$

where the equivalent quality factor is derived from the phase responseof the open-loop transfer function of −G_(m)Z₂₁(jω)

$\begin{matrix}{Q_{eq} = {{\frac{\omega}{2}{\frac{d\left\lbrack {\angle - {G_{m}{Z_{21}\left( {j\; \omega} \right)}}} \right\rbrack}{d\; \omega}}} = \frac{1 + {\left( {k_{m}^{2} - 1} \right)\omega^{4}L_{s}L_{p}C_{1}C_{2}}}{\frac{\omega^{2}L_{p}C_{1}}{Q_{p}} + \frac{\omega^{2}L_{s}C_{2}}{Q_{s}} - {\left( {\frac{1}{Q_{p}} + \frac{1}{Q_{s}}} \right)\omega^{4}L_{s}L_{p}C_{1}C_{2}}}}} & (9)\end{matrix}$

where Q_(p) and Q_(s) are the quality factor of the primary andsecondary winding, respectively. Since the phase noise response isdefined by the equivalent quality factor on the primary side. Note thatEquation 9 has been plotted for the fundamental frequency f₀=30 GHz andas shown in FIG. 12.

Several transformer characteristics are shown in FIGS. 15, 16, and 17. Adiagram illustrating the primary and secondary inductance as a functionof frequency is shown in FIG. 15 where trace 132 represents the primaryand trace 130 represents the secondary inductance as a function offrequency. A diagram illustrating the primary and secondary qualityfactor (Q) as a function of frequency is shown in FIG. 16 where trace140 represents the Q of the primary and trace 142 represents the Q ofthe secondary. A diagram illustrating the transformer coupling factork_(m) as a function of frequency is shown in FIG. 17.

A diagram illustrating the oscillator voltage waveform in differentialmode is shown in FIG. 18 where trace 162 represents the drain voltageV_(D1) on transistor M₁ (FIG. 5) and trace 160 represents the drainvoltage V_(D2) on transistor M₂ which illustrates that the drain voltagecontains both fundamental and 5^(th) harmonics. Note that thefundamental can be rejected or attenuated for the purpose of boostingthe relative importance of the higher harmonic.

A diagram illustrating the oscillator gate voltage waveform is shown inFIG. 19 where trace 150 represents the gate voltage V_(G1) on transistorM₁ (FIG. 5) and trace 152 represents the gate voltage V_(G2) ontransistor M₂.

A diagram illustrating example phase noise of the oscillator circuit ofFIG. 5 is shown in FIG. 23 where trace 190 represents the phase noisefor the high frequency oscillator (e.g., 150 GHz oscillator) 58 (FIG. 5)when it is in free running mode (i.e. not locked); trace 192 representsthe phase noise for the high frequency oscillator (e.g., 150 GHzoscillator) 58 when it is locked to the low frequency (e.g., 30 GHz)oscillator 56 whereby its phase noise follows that of the low frequencyoscillator; and trace 194 represents the phase noise for the lowfrequency oscillator (e.g., 30 GHz). As indicated, the phase noise ofthe oscillator confirms the injection locking theory, therefore thephase noise of the second DCO stage (e.g., the 150 GHz oscillator)follows the phase noise of first DCO stage (e.g., the 30 GHzoscillator).

A diagram illustrating a first example locked signal spectrum of theoscillators is shown in FIG. 24 where trace 200 represents the spectrumof the drain voltage of the low frequency DCO and trace 202 representsthe drain voltage of the high frequency DCO for a value of C_(s)=284 fF(FIG. 5). A diagram illustrating a second example locked signal spectrumof the oscillators is shown in FIG. 25 where trace 204 represents thespectrum of the drain voltage of the low frequency DCO and trace 204represents the drain voltage of the high frequency DCO for a value ofC_(s)=300 fF (FIG. 5). Note that as the secondary capacitor C_(s)increases, the oscillator frequency is reduced since the oscillatorfrequency is a function of one over the square root of LC.

Those skilled in the art will recognize that the boundaries betweenlogic and task blocks are merely illustrative and that alternativeembodiments may merge logic or task blocks or impose an alternatedecomposition of functionality upon various logic or task blocks. Thus,it is to be understood that the architectures depicted herein are merelyexemplary, and that in fact many other architectures may be implementedwhich achieve the same functionality.

Any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality may be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermediary components. Likewise, any two componentsso associated can also be viewed as being “operably connected,” or“operably coupled,” to each other to achieve the desired functionality.

Furthermore, those skilled in the art will recognize that boundariesbetween the above described operations merely illustrative. The multipleoperations may be combined into a single operation, a single operationmay be distributed in additional operations and operations may beexecuted at least partially overlapping in time. Moreover, alternativeembodiments may include multiple instances of a particular operation,and the order of operations may be altered in various other embodiments.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

In the claims, any reference signs placed between parentheses shall notbe construed as limiting the claim. The use of introductory phrases suchas “at least one” and “one or more” in the claims should not beconstrued to imply that the introduction of another claim element by theindefinite articles “a” or “an” limits any particular claim containingsuch introduced claim element to inventions containing only one suchelement, even when the same claim includes the introductory phrases “oneor more” or “at least one” and indefinite articles such as “a” or “an.”The same holds true for the use of definite articles. Unless statedotherwise, terms such as “first,” “second,” etc. are used to arbitrarilydistinguish between the elements such terms describe. Thus, these termsare not necessarily intended to indicate temporal or otherprioritization of such elements. The mere fact that certain measures arerecited in mutually different claims does not indicate that acombination of these measures cannot be used to advantage.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. As numerousmodifications and changes will readily occur to those skilled in theart, it is intended that the invention not be limited to the limitednumber of embodiments described herein. Accordingly, it will beappreciated that all suitable variations, modifications and equivalentsmay be resorted to, falling within the spirit and scope of the presentinvention. The embodiments were chosen and described in order to bestexplain the principles of the invention and the practical application,and to enable others of ordinary skill in the art to understand theinvention for various embodiments with various modifications as aresuited to the particular use contemplated.

What is claimed is:
 1. An oscillator system, comprising: a referencefrequency pulse generator operative to generate a reference signalcontaining a plurality of harmonics; a first oscillator operative toreceive said reference signal output by said pulse generator and togenerate a first fundamental frequency and one or more harmonic signalstherefrom, wherein said first oscillator is injection locked to saidpulse generator; and a second oscillator operative to receive one of theharmonic signals output by said first oscillator, and to generate anoutput signal therefrom, wherein said second oscillator is injectionlocked to said first oscillator.
 2. The oscillator system according toclaim 1, wherein said reference signal generated by said pulse generatorexhibits relatively good phase noise.
 3. The oscillator system accordingto claim 1, wherein said first oscillator's one or more harmonic signalsexhibits relatively good phase noise being injection locked to saidpulse generator.
 4. The oscillator system according to claim 1, whereinsaid second oscillator normally exhibits relatively bad phase noise butis operative to generate said output signal having relatively good phasenoise being injection locked to said first oscillator.
 5. The oscillatorsystem according to claim 1, wherein said second oscillator is operativeto generate relatively high output power at said output node.
 6. Theoscillator system according to claim 1, wherein said second oscillatorexhibits a relatively wide locking range.
 7. An oscillator system,comprising: a pulse generator having relatively good phase noiseoperative to generate a reference frequency signal containing aplurality of harmonics; a first oscillator operative to generate amillimeter wave output fundamental signal along with a higher harmonicsignal, wherein said first oscillator is injection locked to saidreference frequency signal output of said pulse generator; and a secondoscillator normally having relatively poor phase noise operative togenerate an output oscillator signal at an output node having relativelygood phase noise, wherein said second oscillator is injection locked tosaid first oscillator causing the phase noise of said second oscillatorto track that of said first oscillator.
 8. The oscillator systemaccording to claim 7, wherein said second oscillator is operative togenerate relatively high output power at said output node.
 9. Theoscillator system according to claim 7, wherein the phase noise of saidfirst oscillator follows that of said pulse generator.
 10. Theoscillator system according to claim 7, wherein said first oscillatorcomprises a class F oscillator operative to generate a relatively stronghigher harmonic signal.
 11. The oscillator system according to claim 7,wherein said second oscillator exhibits a relatively wide locking range.12. The oscillator system according to claim 7, wherein: the outputfundamental signal is approximately 30 GHz; the higher harmonic signalis approximately 150 GHz; and the output oscillator signal isapproximately 150 GHz.
 13. A method of generating an oscillator signal,comprising: generating a reference frequency signal; first injectionlocking a first oscillator and to the reference frequency signal therebygenerating a millimeter wave first oscillator signal along with aharmonic signal, wherein phase noise of said first oscillator tracksthat of said reference frequency signal; second injection locking asecond oscillator to the harmonic signal and generating an outputoscillator signal therefrom at an output node; and wherein the phasenoise of said second oscillator tracks that of said first oscillator.14. The method according to claim 13, wherein said reference frequencysignal having relatively good phase noise and said second oscillatornormally having relatively poor phase noise.
 15. The method according toclaim 13, wherein: the first oscillator signal is approximately 30 GHz;the harmonic signal is approximately 150 GHz; and the output oscillatorsignal is approximately 150 GHz.
 16. The method according to claim 13,further comprising generating the output oscillator signal to haverelatively high output power at said output node.
 17. The methodaccording to claim 13, further comprising providing said secondoscillator with a relatively wide locking range.
 18. An oscillatorsystem, comprising: a pulse generator having relatively good phase noiseoperative to generate a reference frequency signal having a plurality ofharmonics; a first oscillator operative to receive the referencefrequency signal and to generate a fundamental signal along with ahigher harmonic signal therefrom, wherein said first oscillator isinjection locked to the reference frequency signal output of said pulsegenerator; a second oscillator normally operative to generate a firstoutput oscillator signal at an output node, wherein said secondoscillator is injection locked to said first oscillator causing thephase noise of said second oscillator to track that of said firstoscillator; and a third oscillator operative to generate a second outputsignal, wherein said third oscillator indirectly injection locked tosaid reference frequency signal output of said pulse generator causingthe phase noise of said third oscillator to track that of said pulsegenerator.
 19. The oscillator system according to claim 18, furthercomprising a buffer circuit adapted to receive the signal output of saidthird oscillator and generate a buffered output signal therefrom. 20.The oscillator system according to claim 18, wherein: the firstoscillator signal is approximately 30 GHz; the higher harmonic signal isapproximately 150 GHz; the first output oscillator signal isapproximately 150 GHz; and the second output oscillator signal isapproximately 83 GHz.